Pre-Algebra Examples

$\frac{\frac{15 t^{2} u}{3 r s^{3}}}{\frac{5 t^{3} u^{3}}{6 s^{4}}}$

Step 1

Cancel the common factor of $15$ and $3$ .

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Step 1.1

Factor $3$ out of $15 t^{2} u$ .

$\frac{\frac{3 (5 t^{2} u)}{3 r s^{3}}}{\frac{5 t^{3} u^{3}}{6 s^{4}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $3 r s^{3}$ .

$\frac{\frac{3 (5 t^{2} u)}{3 (r s^{3})}}{\frac{5 t^{3} u^{3}}{6 s^{4}}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{3 (5 t^{2} u)}{3 (r s^{3})}}{\frac{5 t^{3} u^{3}}{6 s^{4}}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{5 t^{2} u}{r s^{3}}}{\frac{5 t^{3} u^{3}}{6 s^{4}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 t^{2} u}{r s^{3}} \cdot \frac{6 s^{4}}{5 t^{3} u^{3}}$

Step 3

Combine.

$\frac{5 t^{2} u (6 s^{4})}{r s^{3} (5 t^{3} u^{3})}$

Step 4

Cancel the common factor of $5$ .

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Step 4.1

Cancel the common factor.

$\frac{5 t^{2} u (6 s^{4})}{r s^{3} (5 t^{3} u^{3})}$

Step 4.2

Rewrite the expression.

$\frac{t^{2} u (6 s^{4})}{r s^{3} (t^{3} u^{3})}$

Step 5

Cancel the common factor of $t^{2}$ and $t^{3}$ .

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Step 5.1

Factor $t^{2}$ out of $t^{2} u (6 s^{4})$ .

$\frac{t^{2} (u (6 s^{4}))}{r s^{3} (t^{3} u^{3})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $t^{2}$ out of $r s^{3} (t^{3} u^{3})$ .

$\frac{t^{2} (u (6 s^{4}))}{t^{2} (r s^{3} (t u^{3}))}$

Step 5.2.2

Cancel the common factor.

$\frac{t^{2} (u (6 s^{4}))}{t^{2} (r s^{3} (t u^{3}))}$

Step 5.2.3

Rewrite the expression.

$\frac{u (6 s^{4})}{r s^{3} (t u^{3})}$

Step 6

Cancel the common factors.

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Step 6.1

Factor $u$ out of $r s^{3} (t u^{3})$ .

$\frac{u (6 s^{4})}{u (r s^{3} (t u^{2}))}$

Step 6.2

Cancel the common factor.

$\frac{u (6 s^{4})}{u (r s^{3} (t u^{2}))}$

Step 6.3

Rewrite the expression.

$\frac{6 s^{4}}{r s^{3} (t u^{2})}$

Step 7

Cancel the common factor of $s^{4}$ and $s^{3}$ .

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Step 7.1

Factor $s^{3}$ out of $6 s^{4}$ .

$\frac{s^{3} (6 s)}{r s^{3} (t u^{2})}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $s^{3}$ out of $r s^{3} (t u^{2})$ .

$\frac{s^{3} (6 s)}{s^{3} (r (t u^{2}))}$

Step 7.2.2

Cancel the common factor.

$\frac{s^{3} (6 s)}{s^{3} (r (t u^{2}))}$

Step 7.2.3

Rewrite the expression.

$\frac{6 s}{r (t u^{2})}$

$\frac{6 s}{r t u^{2}}$